Angular velocity Definition and 841 Threads

Further given: - every beam is infinite stiff - pulleys are massless - cables don't stretch, no slip, and frictionless. -Every pulley has a diameter D except pulley Q. Pulley Q has diameter 0.5*D So what I don't understand is how to calculate/determine the velocity at R and S. Can someone help...

A single pair of points will be in contact between P and Q. The frictional force will try to make the velocity of these points equal. Say the final angular velocity of Q is ωq. The velocity of points in contact can never be equal because of difference in directions of ωq and ωp. If I break...

θ=90°= π /2 so the instantaneous angular velocity dθ/dt= lim∆ t -> 0 (θ(t + ∆ t)-θ(t))/(∆ t) When I calculate it out it is π /2 radians per second. Is this correct?

In a previous thread it was concluded that both torque and angular momentum are taken about a chosen origin, and these quantities are generally not invariant under translations of the origin (since ##\vec{r}## changes but ##\vec{v}## does not, etc.). The moment of inertia tensor doesn't...

Summary:: not constant spin How could I calculate the system lagrangian in function of the generalised coordinates and the conserved quantities associated to the system symmetries? I've been struggling for the case with not constant angular velocity, but I don't realize what I have to do...

Hi there ... How do I calculate the change of angular velocity, when demonstrating conservation of angular momentum? I mean the change of angular velocity depends on the ratio between the two (rotating) masses that moves a distance along radius, and the (rotating) mass of the system itself. In...

As ##P=ccte## we can find final velocity considering a plastic collision ##m_0 . v_0 =(2m+m_0).V## But what about the angular velocity? Because, as the bullet hits the centre of mass of the string, it won't have angular velocity

So this question has something probably due to the conservation of angular momentum. I am able to find the moment of inertia about the pivot, which is : $$\dfrac {1}{3}mL^{2}+\left( \dfrac {1}{12}ML^{2}+mL^{2}\right) =\dfrac {17}{12}ml^{2} $$ Now to find angular velocity when angle =0, how am I...

ω(10)=(1.3)∗(1.0−e^(−10/22) )= 0.475 rad/s 0.475 rad/s=0 +α(10second) α=0.0475 rad/s^2 ∫ω(t)=Θ =1.3t + 28.6e^(-t/22) | (t=10s, t=0) total angle by which the wheel rotates over this period of t=10 seconds = 2.55 rad Θ= 2(pi)(8m)= 1.3t + 28.6e^(-t/22) 0=1.3t + 28.6e^(-t/22) - 2(pi)(8m) t=34...

33.33 RPM (1min/60second)(6.28 radian/1 revolution) = 3.45 rad/s linear velocity=3.45 rad/s * 0.1524m=0.526 m/s linear acceleration= (0.526 m/s)^2 /(0.1524m)=1.814 m/s^2 1.814 m/s^2=(0.1524m)(rotational acceleration) rotational acceleration=11.9 rad/s^2 ω1= (3.45 rad/s)+(11.9rad/s^2)(10s)...

A bicycle wheel rolls at a constant speed along a circular path on a horizontal surface. The wheel has a constant angle of inclination to the vertical direction and the distance from its center of mass G to the fixed Z axis is R. Determine the relationship between the angular velocity w1 around...

I wrote Newton's equations for each body (I took ##x## as the axis aligned with the tension) ##m_1##: ##x)f*_1 -T_1+T_2=0## Where ##f*_1=\omega ^2 r_1## ##m_2## ##x)f*_2 -T_2=0## ##x)f*_2=T_2## Where ##f*_2=\omega ^2 r_2## I wrote that ##T_2=1100 N## and solved for ##\omega##, and I got...

A) The slider experiments three forces, all of them are on the ##x## axis (considering ##x## axis as the axis aligned with the arm): Normal force (exerted by the support), elastic force and centrifugal force, which is ##m.(\omega^2 r)## Elastic force is equal to ##Fe=-k \delta =-2 (R-2R)=2R##...

So first of all, I will have to find the centre of mass. ##X_{cm} = \frac{1}{M}\int x dm## likewise for Y. ##M## =150kg From the above-given points, I can find the equation of a line to be ## y =-\frac{3}{4}x +3## . Area density = ##150kg/(0.5*4*3) = 25kg/m^2## ##X_{cm} = \frac{1}{M}\int x dm...

I have a disc. The center of the disc is its center of mass and the motion of the disc is purely rotational (no translation). What is the angular velocity in the center of the rotating disc?

Hi everyone. Do correct me if I am thinking wrongly. So to find angular velocity, won't I just have to integrate angular acc = 2t, which means angular velocity = t^2? Hence, won't the answer be 3^2=9? The answer seems to be 5.43 :/ Thanks

Is E the correct answer because I think angular velocity is independent of mass distribution of the object? Thanks

Problem Statement: How to calculate minumum angular velocity of a mass on a spinning plate Relevant Equations: f=mrw^2 Hi, here's the question: a) A rough horizontal plate rotates with a constant angular velocity of w about a fixed vertical axis. A particle of mass m lies on the plate at a...

Problem Statement: The uniform 4-kg cylinder A, of radius r = 150 mm, has an angular velocity w = 50 rad/s when it is brought into contact with an identical cylinder B which is at rest. The coefficient of kinetic friction at the contact point D is uk. After a period of slipping, the cylinders...

Hi, a newbie to the site and hoping someone can help. Its been a long time since I studied physics or math at school. I am having some difficulty calculating the angular velocity of the arm trhough a partial movement (phase). The data set I have separates the angular velocity into the three...

It seems to me that this transition implies going from kinetic friction to static friction. The kinetic friction would apply a torque that would slow down the object's angular velocity, but I'm not sure how this connects to the object suddenly transitioning into rotating without slipping.

(i) A rotating machine shaft turns through 2100 revolutions in 3 minutes. Determine the average angular velocity, w, of the machine shaft in rad/s. the answer for this is 2100 x 2 pie = 4200 pie radian 3 mins = 180 seconds 4200 / 180 = 73.3 rad/s (ii) Determine the area and arc length of the...

Hi i am e-pie's brother and he let me use his account.Since $$\vec{\omega}$$ is always perpendicular to the plane.Shouldn't this be $$0^o$$?

Lets consider the angular momentum tensor (here ##m=1##) \begin{equation} L^{ij} = x^iv^j - x^jv^i \end{equation} and rortational velocity of particle (expressed via angular momentum tensor) \begin{equation} v^j = \omega^{jm}x_m. \end{equation} Then \begin{equation} L^{ij} =...

I am strugglin with this step in my assignment. I am dealing with a centrifuge with a known moment of inertia. I should write the expression for a torque of the motor and express it as a function of angular velocity. Can you help me please?

Homework Statement Finding the general formula for max angular velocity ( answers say 0.839*(g/b)) but I do not understand how Homework Equations 0.839*(g/b) The Attempt at a Solution

think of a engine. it has a flywheel and a rod connected to it. a string had been totally wrapped around the rod and a mass is hanged from the very end of the rod. the system is in equilibrium. but as the engine starts to rotate, the rod with rotate as well and cause the hanged object to go...

Homework Statement A solid body begins to rotate around a fixed axis with angular acceleration ##\beta=\beta_0\cosφ##, where ##\beta_0## is a constant vector, ##φ##, is the angle of rotation of the body from initial position. Determine the angular velocity of this body as a function of the...

Homework Statement A ball A is rotating on a table with an angular velocity ω about its vertical axis. An identical ball B collides with the ball A elastically. After collision the ball A starts sliding over the table. The coefficient of friction is µ. Find: 1) the angle α between the angular...

Homework Statement Homework Equations ##v=\omega r## The Attempt at a Solution So, using the equation, one can work out the velocity at point ##B##. ##v_B=\omega_{AB} \cdot r_B## ##v_B=6(0.4)=2.4~ ms^{-1}##I then tried working out the angular velocity at point ##C## using the instantaneous...

Homework Statement I have been set this question and I am struggling with parts b and c. I think I am nearly there but can't quite get over the line. Please could someone give me a nudge in the right direction. [/B] 1. (a) For the mechanism shown in FIGURE 1 determine for the angle θ = 45°: (i)...

Homework Statement A uniform cylindrical wheel of mass ##m_{1}## and radius ##R_{1}## rotates with angular velocity ##\omega_{1}##. It lies a certain distance (along the same axis) from a static wheel of radius ##R_{2}## and mass ##m_{2}##. The wheels are then pushed against each other with a...

Homework Statement AB is a rod of length 10 m that is leaning against the wall. Given variables are shown in the diagram. Find angular velocity of A wrt B. https://imgur.com/a/8bEdYhN I have a doubt in one step that I will highlight in "The attempt at a solution" part. Homework Equations...

Homework Statement A pendulum with a light rod of length ##l## with a bob of mass ##m## is released from rest at an angle ##\theta_0## to the downward vertical. Find its angular velocity as a function of θ, and the period of small oscillations about the position of stable equilibrium. Write...

I have seen so many questions and confusion about the difference between angular velocity/speed and angular frequency. Usually, answers were always given in the context of uniform circular motion (angular speed) and simple harmonic oscillation (angular frequency), but this is what causes the...

Homework Statement A particle is moving parallel to x-axis in the positive direction with velocity v such that at all the instants the y -axis component of its position vector is constant and is equal to 'b'. Find angular velocity about origin. Homework EquationsThe Attempt at a Solution I...

Angular velocity is the rate of angular displacement about an axis. Its direction is determined by right hand rule. According to right hand rule, if you hold the axis with your right hand and rotate the fingers in the direction of motion of the rotating body then thumb will point the direction...

Homework Statement Homework Equations $$\mathcal{L}=T-U$$ $$\omega= \frac{d\phi}{dt}$$ $$I=mr^{2}$$ The Attempt at a Solution My problem is not finding the Lagrangian. But finding the kinetic energy! The translational kinetic energy would obviously be the following: $$K.E...

From a wiki's vis-viva equation page, it is given that the specific angular momentum h is also equal to the following: h = wr^2 = ab * n How can ab * n be derived to be equal to the angular momentum using elliptical orbit energy/momentum/other equations without having to use calculus or...

Homework Statement 4 persons each with mass m stand out on the edge of the carousel that rotates with angular velocity W0. carousel has mass 4m, radius r and inertia I = 2mr^2. The 4 persons then go all the way to the center of the carousel. Show that the final angular velocity W1 = 3W0 See...

Hello all, I was doing some behavioural modelling of the torque transfer characteristics of a belt drive system from the driver pulley to the driven pulley. While doing the same, i have tried to see how the angular velocity is getting transferred as well. I would explain my point with the...

Homework Statement In the document below I need to try and find the angular velocity I need help on part b Homework Equations F=ma KE_Translational= 0.5mv^2 KE-Rotational= 0.5Iw^2 Assuming g=10m/s^2 The Attempt at a Solution I have the answer key attached with the question but I am not sure...

I hope many here know about vortex tube and its application. I myself have done some study but were unable to find one answer. If we know the speed of the inlet fluid, then how can the angular velocity of the fluid during its rotational motion can be determined.

Homework Statement Why do the left wheels of a car rise when it takes a sharp left turn (that is it lurches towards the right)? Homework Equations $$a_c= V^2/R$$The Attempt at a Solution I started by imagining the car as being a part of a very large ring, dx. Since it's taking a left turn...

Homework Statement Starting from the center of a circular path of radius R, a particle P chases another particle Q that is moving with a uniform speed v on the circular path. The chaser P moves with a constant speed u and always remains collinear with the centre and location of the chased Q...

When I rotate my head with 1rad/s , I can see a body which 350000km away have velocity greater than c.is that possible?

I was reading that gyroscopes can be used to measure the angular velocity of precession, such as in the Hubble space telescope, but mathematically how can this be done? Many thanks

Homework Statement Homework Equations [/B] T = inertia * alpha The Attempt at a Solution I'm not sure how the torque or angular velocity initially affects the time to speed, but it seems like the more angular velocity , then the quicker the engine would stop. I do know that more torque...

I read in several places that if, for example, a point particle exhibits uniform circular motion about the z-axis within an osculating plane not equal to the x,y plane, then the angular velocity still points along the z-axis, even though the angular momentum does not (it precesses about the...